Locally Recoverable Codes on Algebraic Curves

Alexander Barg*, Itzhak Tamo, Serge Vladut

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


A code over a finite alphabet is called locally recoverable (LRC code) if every symbol in the encoding is a function of a small number (at most $r$ ) of other symbols of the codeword. In this paper, we introduce a construction of LRC codes on algebraic curves, extending a recent construction of the Reed-Solomon like codes with locality. We treat the following situations: local recovery of a single erasure, local recovery of multiple erasures, and codes with several disjoint recovery sets for every coordinate (the availability problem). For each of these three problems we describe a general construction of codes on curves and construct several families of LRC codes. We also describe a construction of codes with availability that relies on automorphism groups of curves. We also consider the asymptotic problem for the parameters of the LRC codes on curves. We show that the codes obtained from asymptotically maximal curves (for instance, Garcia-Stichtenoth towers) improve upon the asymptotic versions of the Gilbert-Varshamov bound for LRC codes.

Original languageEnglish
Article number7918640
Pages (from-to)4928-4939
Number of pages12
JournalIEEE Transactions on Information Theory
Issue number8
StatePublished - Aug 2017
Externally publishedYes


  • Asymptotic bounds
  • Codes for distributed storage
  • Codes with availability
  • Covering maps
  • Hermitian curves


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